Variational Phase-Field Models of Fracture

Blaise Bourdin, Louisiana State University
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Abstract: Phase-field models of fracture, which I developed as numerical techniques for Francfort and Marigo's reformulation of Griffith fracture have become some of the most popular techniques in fracture mechanics. In this talk, I will quickly derive Francfort and Marigo's variational approach to fracture and its phase-field approximation. I will then discuss their numerical implementation, illustrated with quantitative validation and verification examples on a broad range of applications. Finally, I will discuss recent extensions, the computational challenges that they pose, and the insight they provide on challenging topics such as crack nucleation in quasi-brittle materials and propagation in heterogeneous materials.

Blaise Bourdin A.K. & Shirley Barton Professor of Mathematics Louisiana
State University

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